Some adaptations of the Latin alphabet are augmented with ligatures, such as æ in Old English and Icelandic and Ȣ in Algonquian ; by borrowings from other alphabets, such as the thorn þ in Old English and Icelandic, which came from the Futhark runes ; and by modifying existing letters, such as the eth ð of Old English and Icelandic, which is a modified d. Other alphabets only use a subset of the Latin alphabet, such as Hawaiian, and Italian, which uses the letters j, k, x, y and w only in foreign words.

: For any set A there is a function f such that for any non-empty subset B of A, f ( B ) lies in B.

For example, suppose that each member of the collection X is a nonempty subset of the natural numbers.

The reason that we are able to choose least elements from subsets of the natural numbers is the fact that the natural numbers are well-ordered: every nonempty subset of the natural numbers has a unique least element under the natural ordering.

Similarly, although a subset of the real numbers that is not Lebesgue measurable can be proven to exist using the axiom of choice, it is consistent that no such set is definable.

** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

** Every infinite game in which is a Borel subset of Baire space is determined.

** The Vitali theorem on the existence of non-measurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable.

Some say that literary criticism is a subset of literary theory.

Similarly, the subset order ⊆ on the subsets of any given set is antisymmetric: given two sets A and B, if every element in A also is in B and every element in B is also in A, then A and B must contain all the same elements and therefore be equal:

In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable.

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

This is clearly a deficiency in T.

The second situation is illustrated by the operator T on Af ( F any field ) represented in the standard basis by Af.

The characteristic polynomial for A is Af and this is plainly also the minimal polynomial for A ( or for T ).

Thus T is not diagonalizable.

If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

( B ) each Af is invariant under T ; ;

( C ) if Af is the operator induced on Af by T, then the minimal polynomial for Af is Af.

It is certainly clear that the subspaces Af are invariant under T.

If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

Was it supposed, perchance, that A & M ( vocational training, that is ) was quite sufficient for the immigrant class which flooded that part of the New England world in the post-Civil War period, the immigrants having been brought in from Southern Europe, to work in the mills, to make up for the labor shortage caused by migration to the West??

I know you are very busy now, you are writing a great deal & your book is coming out, isn't it??

There is a workable alternative to this potentially dangerous and harmful C. & O. - B. & O. merger scheme '' --

The logic of creating a strong, balanced, competitive two-system railroad service in the East is so obvious that B. & O. was publicly committed to the approach outlined here.

Several efforts were made in this direction, and though not all of them survive to this day, the Brown & Sharpe wire gage system was eventually adopted as the American standard and is still in common use today.

The original machine, bearing its famous serial number, is still on exhibition at the Brown & Sharpe Precision Center in Providence.

The Machine Tool Division is currently producing Brown & Sharpe single spindle automatic screw machines, grinding machines of many types, and knee and bed-type milling machines.

Recently added is the Brown & Sharpe turret drilling machine which introduces the company to an entirely new field of tool development.

The most intriguing aspect of the S & W Magnum chambered for the new Jet is that it can also fire standard

Besides flathead bronze screws, silicon bronze Stronghold nails ( made by Independent Nail & Packing Co., Bridgewater, Mass. ) are used extensively in assembly and Weldwood resorcinol glue is used in all the joints.

Harold E. Strang, expert in switchgear design, for a long period vp & gm of the Measurements & Industrial Products Division, and who currently, approaching retirement, is vice-president and consulting engineer in the Switchgear & Control Division.

Its president is Otis M. Waters, partner in the law firm of Timen & Waters, 540-K Chrysler Bldg., New York City.

Not a year goes by but what several local companies in the U.S. and Canada, even overseas, write to Fueloil & Oil Heat to inquire if it's feasible and where it is being done.

The Barker index is published for the Barker Index Committee by W. Heffer & Sons, Ltd., 4 Petty Cury, Cambridge, England.

The monthly cost of ADC to more than 100,000 recipients in the county is 4.4 million dollars, said C. Virgil Martin, president of Carson Pirie Scott & Co., committee chairman.

-- Held out of Texas Tech's sweat-suits drill Monday at Lubbock was tackle Richard Stafford, who is undergoing treatment for a leg injury suffered in the Raiders' 38-7 loss to Texas A & M Because of its important game with Arkansas coming up Saturday, Baylor worked out in the rain Monday -- mud or no mud.

A publicity release from Oregon Physicians Service, of which Harvey is president, quoted him as saying the welfare office move to Salem, instead of `` crippling '' the agency, had provided an avenue to correct administrative weaknesses, with the key being improved communications between F & A and the commission staff.

C & O president Walter J. Tuohy was summoned back for cross-examination by New York Central attorneys before examiner John Bradford who is hearing the complex case.

The report is based on a survey by Blyth & Company, investment bankers.

* Austin & Ally is an American sitcom that first aired on the Disney Channel in Winter 2011.

It was the mutual bond and obligation between monarch and subjects, whereby subjects are called his liege subjects, because they are bound to obey and serve him ; and he is called their liege lord, because he should maintain and defend them ( Ex parte Anderson ( 1861 ) 3 El & El 487 ; 121 ER 525 ; China Navigation Co v Attorney-General ( 1932 ) 48 TLR 375 ; Attorney-General v Nissan 1 All ER 629 ; Oppenheimer v Cattermole 3 All ER 1106 ).

Natural allegiance and obedience is an incident inseparable to every subject, for parte Anderson ( 1861 ) 3 El & El 487 ; 121 ER 525 ).